The University of California is struggling with budget woes that have deeply affected campus life. Yet the system’s nine colleges still lead the nation in providing top-flight college education to the masses.

At many other colleges, poor and truly middle-class students remain a distinct minority. Affluent students predominate at liberal-arts colleges like Oberlin and Bates, private universities like Cornell and Texas Christian and even many public universities, including Wisconsin, Penn State and Georgia Tech. The University of California, by contrast, enrolls a large number of high-performing students of all economic backgrounds.

That contrast is the most striking result of this year’s College Access Index, a New York Times measure of economic diversity at top colleges. Six of the top seven spots in this year’s index belong to University of California campuses, with Irvine at No. 1, and the flagship Berkeley campus at No. 7.

The index is based on three factors: the share of students receiving Pell grants (which typically go to families making less than $70,000); the graduation rate of those students; and the net cost, after financial aid, that a college charges low- and middle-income students. The index covers 179 of the nation’s top colleges, defined as having an overall five-year graduation rate of at least 75 percent.

Economic diversity has become a much-debated topic lately. Academic research has shown that many high-achieving low-income students do not attend a selective college, even when they’re qualified. They instead enroll at a college closer to their home, with fewer resources – and many don’t end up getting a four-year degree. This educational divide is a major reason that climbing the income ladder remains so hard.

“The big challenge for American higher education,” Howard Gillman, a political scientist who is the chancellor at the University of California at Irvine, told me, “is that it has to be a gateway through which talented young people can thrive, regardless of their background.”

Officials at other top colleges, for their part, often say that they want to enroll more of these talented low- and middle-income students. But only some colleges have followed up these words with actions.

Tellingly, the colleges enrolling more diverse student bodies – not just in terms of race, religion and geography, but social class as well – don’t fit any one model. Some are small, and some large. Some are rural, and some urban. Some are extremely selective, with enormous endowments, and some are less so.

Video

Madison Ramirez Mazaheri talks about what it was like being placed in remedial classes because she was an immigrant.

You can see the contrast between otherwise similar colleges. Amherst and Wesleyan are more diverse than Williams and Colby; Holy Cross more so than Notre Dame. The flagship state universities in Texas and North Carolina are more diverse than those in Michigan, Virginia and Wisconsin.

This variety suggests that economic diversity is within the power of any top university. The question is whether the university’s leaders decide it’s a priority.

Among the most notable patterns from this year’s College Access Index:

Economic diversity has stagnated. The median share of first-year students receiving Pell grants at these colleges was 17 percent last year. That was up marginally from 16 percent the previous academic year, but unchanged from 17 percent the prior two years.

This stagnation means that many elite colleges remain overwhelmingly well-off. For every student from the entire bottom half of the nation’s income distribution at Dartmouth, Penn, Princeton, Yale and more than a few other colleges, there appear to be roughly two students from just the top 5 percent (which means they come from families making at least $200,000).

College administrators wouldn’t phrase it this way, yet they are essentially deciding that economic diversity matters less than other priorities – like sports teams, new buildings and some low-enrollment academic programs.

But a small number of colleges have made big changes. At Pomona, the share of first-year students receiving Pell grants rose to 22 percent last year, from 16 percent three years earlier. The share has also risen notably at Davidson, in North Carolina; Franklin & Marshall, in Pennsylvania; and St. Olaf, in Minnesota.

Video

Casey Hammond, a high school senior, describes growing up in a rural area with a mother who was in high school herself when he was born.

Stonehill, in Massachusetts, had the biggest jump in Pell students, by focusing on candidates within 50 miles of campus and increasing financial aid. “It enhances the education of all students to meet people who are different than they are,” Eileen O’Leary, a Stonehill administrator, said.

Of course, the overall stagnation in the numbers means that for almost every college that’s becoming more diverse, another college is becoming less so. The share of Pell recipients at Duke, Harvard, Rice, Williams and even most University of California campuses has fallen somewhat since 2011.

Most low-income students who attend top colleges thrive. Merely going to college isn’t enough to change a teenager’s life. The benefits of college – higher income, better health, greater life satisfaction – generally depend on graduating, research shows. Which is one reason you sometimes hear worries about whether low-income students can fit in at top colleges.

But the evidence suggests that they can and do.

The median six-year graduation rate for Pell students at the colleges in our index is 84 percent, only slightly lower than the overall rate of 85 percent. College certainly involves challenges for many low-income students, but they largely meet them when they attend a top college. That’s a big reason these colleges matter: They don’t leave many students saddled with the toxic combination of debt and no degree.

On some campuses, the Pell graduation rate even exceeds the overall rate. One of them is the University of California at Irvine.

Irvine’s story is fascinating. It owes its existence to California’s population explosion after World War II, which created a quandary for the state’s public universities. Either they had to step back from their historic mission – and educate a much smaller share of California teenagers – or they had to grow enormously.

Despite the costs, a bipartisan group of state leaders chose expansion. On June 20, 1964, one day after the Civil Rights Act passed, President Lyndon B. Johnson joined state officials in a previously unincorporated patch of Orange County to dedicate the Irvine campus. The new campus’s raison d’etre, as with new ones in San Diego and Santa Cruz, was to provide a college education for the masses.

Throughout, the University of California took deliberate steps to attract students of modest means. It kept tuition low and did far more to recruit community-college transfers than most elite state universities. The transfer pipeline is crucial, because many highly qualified low-income students— unaware of how much financial aid is available at some four-year colleges — first enroll at a local community college, where published tuition tends to be low.

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Basti Lopez, center, started at Santa Ana College before transferring to Irvine. She now works at Santa Ana helping other students with the transfer process.CreditTroy Harvey for The New York Times

“For a lot of first-generation students, it’s very hard for parents to understand how to help their child prepare for college expenses,” said Basti Lopez, who emigrated with her parents from Mexico as a child and graduated from Irvine in May.

She had started at Santa Ana College, a two-year college, before applying to four-year colleges as a junior transfer. She was admitted to Berkeley, Irvine and Santa Cruz and chose Irvine, both because of the financial-aid package and because it was closer to home. She is now back working at Santa Ana, helping students with the transfer process, and she’s studying for the law-school admission exam, hoping to become an immigration lawyer.

Students like Ms. Lopez are one reason that Irvine’s student body includes more students with Pell grants than all eight colleges of the Ivy League combined.

It’s true that the California colleges have a built-in advantage: the many high-performing students from immigrant families who live there. But that’s hardly the only reason for the economic diversity. The University of California’s aggressive steps to recruit, admit, enroll and support low-income students are also crucial.

And yet American society seems to be making less of this broad effort than it once did.

California, rather than making another push to bring college to the masses, is taking small steps in reverse. With state funding declining, the University of California has been enrolling fewer in-state students (even as the population keeps growing) and a greater number of affluent students from other countries and states. Outside California, the educational gap between rich and poor is much wider – and not narrowing very rapidly.

Video

Thomas Hiura explains the struggle of telling his working-class high school classmates why it is worth $62,000 a year for a liberal arts degree.

All the while, a college education remains the most reliable ticket to the middle class and beyond. The unemployment rate for college graduates is only 2.7 percent, and the pay gap between college graduates and everyone else is near a record high.

College obviously can’t solve all of the economy’s problems, but there is a reason that nearly all families that can comfortably send their children to college do so. For families that aren’t as comfortable, some colleges are doing much more to help than others.

Correction:Sept. 17, 2015

An earlier version of this article misstated one of the colleges to which Basti Lopez was accepted as a transfer student. It was Santa Cruz, not Santa Clara.

Coming soon: A more detailed look at the least economically diverse colleges on our list.

A version of this article appears in print on , on Page A3 of the New York edition with the headline: California’s Universities, Still a Source of Opportunity. Order Reprints | Today’s Paper | Subscribe